Comparing the Optimization Methods#

[1]:

# import libraries
import jax.numpy as jnp
from optymus.benchmark import methods_comparison

[2]:

from optymus.benchmark import HimmeblauFunction

# define the objective function
f = HimmeblauFunction()

# define the initial point
initial_point = jnp.array([0, 5])

f.plot()

../../_images/examples_notebooks_4.methods_comparison_2_0.png

[3]:

comparison = methods_comparison(f, initial_point, verbose=False, max_iter=100)

100%|██████████| 11/11 [02:11<00:00, 11.98s/it]

[4]:

comparison['results']

[4]:

	method	x_opt	f_min	n_iter	time
0	Gradient Descent	[-2.8051180808608414, 3.131312517644538]	1.2151348386129352e-15	5	0.197249
1	Univariant	[-2.8051180976907424, 3.1313125184240542]	3.74326772617301e-15	3	0.259626
2	BFGS	[-2.8051181454077057, 3.131313798010024]	6.588583976279607e-11	4	0.277029
3	Conjugate Gradients (fletcher_reeves)	[-2.8051180908358573, 3.1313124657578117]	1.1158273896131452e-13	3	0.311757
4	Powell	[-2.8051181469023305, 3.131312584887037]	2.9009608415117576e-13	2	0.554102
5	Newton-Raphson	[2.999999999996896, 2.0000000000133182]	2.545076537982263e-21	5	1.122987
6	Adagrad	[-1.9076663457910115, 3.6954353270806095]	35.98393817255608	100	2.003074
7	Adamax	[-2.822263741759333, 3.1272400512420284]	0.010357710402059517	100	2.009426
8	RMSprop	[-0.09997346539296385, -0.09990007036924864]	173.25400825979125	100	2.020720
9	Yogi	[-1.0154588800168631, 4.1608946545268575]	120.17736216526826	100	2.102989
10	Adam	[-2.793052990299834, 3.140203199556635]	0.008040011808338025	100	2.206574

[5]:

from optymus.plots import plot_optim

plot_optim(f_obj=f, x0=initial_point, comparison=comparison, show=True, notebook=True,)

Data type cannot be displayed: application/vnd.plotly.v1+json

McCormick Function#

[6]:

from optymus.benchmark import MccormickFunction

# define the objective function
f = MccormickFunction()

# define the initial point
initial_point = jnp.array([2, 2])

f.plot()

../../_images/examples_notebooks_4.methods_comparison_7_0.png

[7]:

comparison = methods_comparison(f, initial_point, verbose=False, max_iter=100, learning_rate=0.01)

100%|██████████| 11/11 [02:24<00:00, 13.12s/it]

[8]:

comparison['results']

[8]:

	method	x_opt	f_min	n_iter	time
0	Gradient Descent	[2.5943825933594176, 1.5944038260303497]	1.2283696990657877	4	0.233018
1	BFGS	[2.5943948334728786, 1.5943947965070397]	1.2283696986089008	3	0.246913
2	Conjugate Gradients (fletcher_reeves)	[2.59439519159073, 1.5943950366170843]	1.2283696986087804	3	0.325162
3	Newton-Raphson	[2.594395110694578, 1.5943950969522729]	1.2283696986087564	3	0.602443
4	Univariant	[2.5943970420151112, 1.594395887784954]	1.228369698613304	7	0.683610
5	Powell	[2.5943950741665596, 1.5943950813799577]	1.2283696986087578	3	1.009171
6	Yogi	[2.555939012230438, 1.5550882690033252]	1.230948387588903	100	1.697698
7	RMSprop	[-0.00999988470984365, 0.010000139346239431]	1.0404004310290038	100	1.870464
8	Adamax	[2.487798183908959, 1.5761850655233682]	1.2427562491630404	100	2.507063
9	Adagrad	[2.1728539774681885, 1.82971360617863]	1.6742700801208086	100	2.556201
10	Adam	[2.557998679942181, 1.5558893847834132]	1.2307673475752892	100	2.607516

[9]:

from optymus.plots import plot_optim

plot_optim(f_obj=f, x0=initial_point, comparison=comparison, show=True, notebook=True)

Data type cannot be displayed: application/vnd.plotly.v1+json